Sergey Alexeyevich Chaplygin (; 5 April 1869 – 8 October 1942) was a Russian and Soviet physicist, mathematician, and mechanical engineer. He is known for mathematical formulas such as Chaplygin's equation and for a hypothetical substance in cosmology called Chaplygin gas, named after him.
He graduated in 1890 from Moscow University, and later became a professor. He taught mechanical engineering at Moscow Higher Courses for Women in 1901, and of applied mathematics at Moscow School of Technology, 1903. He was appointed Director of the courses in 1905. Leonid I. Sedov was one of his students.
Chaplygin's theories were greatly inspired by N. Ye. Zhukovsky, who founded the Central Institute of Aerodynamics. His early research focused on hydromechanics. His "Collected Works", consisting of 4 volumes, were published in 1948.
After graduating from the university, he went on to become a professor there. In 1897, he published On the motion of a heavy body of revolution in a horizontal plane, which was the first to present the general equation of motion of a nonholonomic system. This equation is a generalisation of Lagrange's equation. In 1899, he was awarded the Gold Medal of the St. Petersburg Academy of Sciences.
Death
thumb|Grave of Sergey Chaplygin
Chaplygin died of a brain haemorrhage in October 1942.